The works such as [1]}, [2]}, [3]} mainly focus on the ratio of infectious dynamic which is based on a large amount of individuals. In order to explain the spreading process in networks, multiple stochastic models are proposed. One line is to model it by Markov theory [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}. Among such spreading models, the majority of the works discusses the SIS epidemic process and attempts to reach disease-free equilibrium (DFE), which means the equilibrium point without infections. In order to reach DFE, the curing rate in the network should be high. In particular, the basic reproduction number in the network needs to be less than or equal to one [10]}. The pandemic and recovery speeds are determined by contact network structure. By minimizing the spectral norm of the transition matrix, the epidemic spreading process can be suppressed [7]}, [8]}, [9]}. Moreover, by combining the protection resources such as vaccines or antidotes, the cost-optimal resources distribution problem is studied in SIS [9]} and SIR [11]} processes. In [12]}, the typical SIS process is extended to Susceptible-Exposed-Infected-Vigilant (SEIV) epidemic process. A model predictive controller is proposed to extinct the SEIV process, meanwhile, minimizing the control resource cost.
